Problem: Given $ m \angle RPS = 3x + 18$, $ m \angle QPR = 3x + 93$, and $ m \angle QPS = 141$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {3x + 93} + {3x + 18} = {141}$ Combine like terms: $ 6x + 111 = 141$ Subtract $111$ from both sides: $ 6x = 30$ Divide both sides by $6$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 3({5}) + 93$ Simplify: $ {m\angle QPR = 15 + 93}$ So ${m\angle QPR = 108}$.